why do electrical devices have to be grounded?

The metal case is connected to ground so that there will be a short circuit if the live terminal comes into contact with the metal case. This should blow fuses and/or trip circuit breakers. Otherwise the metal case would become live and could kill you if you touched it. This happens all too often.
The power for the device is delivered via the live and neutral terminals.

You don't HAVE to ground an electrical device.  Its is a safety precaution. The chassis of most appliances IS connected to the grounding pin of a 3-prong plug.  The two other prongs are used to deliver power to the device.  In normal operation, there is no current or voltage present on the case of the device, but in the even of a fault (gound fault) dangerous voltages/currents may exist and are routed safely to gound.

Also, my book says that there is a ground connected to the metal casing of an electrical device, then that is connected to the ground prong of the wall. If it is grounded, how is it powering the device? And how come the current doesn't shock you on the casing when its on it's way to the ground?

The black wire in the receptacle is ?hot?. This means the voltage in the this wire = 120 v. The white wire in the receptacle is neutral. This means the voltage in the this wire = 0 v. The potential difference between these 2 wires = 120 v. The bare copper wire in the receptacle is the ground wire. If you look inside the receptacle, you will see that the bare copper wire is not attached to the black or white wire. The bare copper wire is connected to the body of the receptacle. If you open the circuit breaker box or fuse box, you can see that the bare copper wire is not connected to the either end of the breakers or fuses. If you look at the electric meter, outside your house, you will an aluminum wire going from the bottom of the meter box to the ground. When the meter was installed, a 6 ft copper rod was pounded into the ground below the meter. All the bare copper wires are connected to the aluminum entrance cable, which is connected to the ground rod.  I will refer to this later!

When you plug in a 1500 watt electric compressor, how much current flows through the wires in the motor of the compressor?
P = V * I
1500 = 120 * I, I = 12.5 amps
When the compressor is operating, 7.5 amps of current flows through the wires in the motor of the compressor.  The ground wire is not connected to the wires in the motor or to the black wire. So normally, no electric current flows through the ground wire.

When an electric appliance has a short, this means that electric current can flow from the black wire or the wires in the motor to the metal body of the appliance. When you turn on the compressor, the metal body is ?hot?. This means the voltage of the metal is 120 v. When you touch the metal handle, the 120 volts will force electric current to flow from the handle into your hand. You would be shocked, if the bare copper was not connected to the ground prong of the wall. The resistance of the ground wire is much less than the resistance of your skin. So, the current will flow through the ground wire in the compressor, through the ground wire in the receptacle, to the breaker or fuse box. The breaker will flip off or the fuse will melt. Now the voltage of the receptacle is 0 volts.

If the breaker does not flip off or the fuse does not melt, the current will flow to the meter and down the 6 ft copper rod. By that time, the main breaker should flip off.

See the website below for diagrams and an explanation.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/bregnd.html